THE DAUGAVET PROPERTY IN REARRANGEMENT INVARIANT SPACES

被引：0

作者：

Acosta, M. D. ^{[1
]}

Kaminska, A. ^{[2
]}

Mastylo, M. ^{[3
,4
]}

机构：

[1] Univ Granada, Dept Anal Matemat, E-18071 Granada, Spain

[2] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[3] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

[4] Polish Acad Sci, Inst Math, Poznan Branch, PL-61614 Poznan, Poland

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 367卷 / 06期

关键词：

Daugavet property; rearrangement invariant spaces; Orlicz spaces; uniform monotonicity; BANACH-LATTICES; MONOTONICITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study rearrangement invariant spaces with the Daugavet property. The main result of this paper states that under mild assumptions the only nonseparable rearrangement invariant space X over an atomless finite measure space with the Daugavet property is L-infinity endowed with its canonical norm. We also prove that a uniformly monotone rearrangement invariant space over an infinite atomless measure space with the Daugavet property is isometric to L-1. As an application we obtain that an Orlicz space over an atomless measure space has the Daugavet property if and only if it is isometrically isomorphic to L-1.

引用

页码：4061 / 4078

页数：18

共 17 条

[1]

Abramovich Y. A., 2002, GRADUATE STUDIES MAT, V50

[2]

Acosta MD, 2012, J CONVEX ANAL, V19, P875

[3]

[Anonymous], 1996, DISS MATH

[4]

Bennett C., 1988, Pure Appl. Math., V129

[5]

Daugavet IK., 1963, USP MAT NAUK, V18, P157

[6] Monotonicity and rotundity properties in Banach lattices [J].

Hudzik, H ;

Kaminska, A ;

Mastylo, M .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2000, 30 (03) :933-950

[7]

Ivakhno Y, 2007, MATH SCAND, V101, P261

[8] Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces [J].

Kadets, Vladimir ;

Martin, Miguel ;

Meri, Javier ;

Werner, Dirk .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (02) :331-348

[9] Banach spaces with the Daugavet property [J].

Kadets, VM ;

Shvidkoy, RV ;

Sirotkin, GG ;

Werner, D .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (02) :855-873

[10] The Dunford-Pettis property for symmetric spaces [J].

Kaminska, A ;

Mastylo, M .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2000, 52 (04) :789-803

← 1 2 →